In theory, a light-emitting diode (LED) may emit optical power higher than the driving electrical power, with the difference between the optical power and electrical power drawn from lattice heat. In other words, an LED's wall-plug efficiency η, which is the ratio of optical output power to electrical input power, that is greater than 100%. This phenomenon is known as electro-luminescent cooling, electro-luminescence refrigeration, opto-thermionic cooling, the operation of a “Thermischer Konverter,” and thermo-photonic cooling.
In an electro-luminescently cooled LED, electrons and holes are first excited by small forward bias voltage V, which may be small enough that qV<hω, where q is the charge of an electron and hω is the energy of the emitted photon. The total amount of electrical work supplied per excitation is the product of the electron's charge q and the bias voltage V; when qV is zero, the device is in thermodynamic equilibrium. Upon excitation, some of the electrons and holes relax by radiative recombination and generate photons that exit the LED. The fraction of electrons and holes that relax by radiative recombination is defined as the external quantum efficiency ηEQE. If each injected electron-hole pair emits a photon of energy hω with an external quantum efficiency ηEQE but requires just qV in work for excitation, the wall-plug efficiency η may be expressed as:
      η    =                  ℏ        ⁢                                  ⁢        ω            qV        ⁣      ·          η      EQE      
The observation of light emission with photon energy hω in excess of the electrical input energy per electron qV is readily accessible in LEDs at a variety of wavelengths. At these operating points, the electron population is pumped by a combination of electrical work and Peltier heat originating in the semiconductor's lattice; this thermo-electric heat exchange is non-uniformly distributed throughout the device. This phenomenon has been experimentally observed in a SiC emitter and connected physically to the Peltier effect. Nevertheless, net cooling, or equivalently electro-luminescence with wall-plug efficiency greater than unity, has eluded direct observation until recently.
Early measurements of light emission from semiconductor diodes were followed closely by theoretical developments. Beginning in 1957, a body of literature theoretically establishing the basic thermodynamic consistency of electro-luminescent cooling and exploring its limits began to emerge. In 1964, experimental results demonstrated that a GaAs diode could produce electro-luminescence with an average photon energy 3% greater than qV. Still, net cooling was not achieved due to competing non-radiative recombination processes, which led to a conclusion that a high value of ηEQE was required for direct experimental observation of net electro-luminescent cooling.
More recently, several modeling and design efforts have aimed to raise the external quantum efficiency ηEQE toward unity by maximizing the fraction of recombination that is radiative and employing photon recycling to improve photon extraction. More recent attempts to observe electro-luminescent cooling experimentally with a wall-plug efficiency η near 100% have focused on the regime in which qV is equal to at least 50% of the material bandgap Eg≈hω. As qV is lowered well below Eg, the electron and hole populations decrease exponentially following a Boltzmann distribution with decreasing chemical potential. Since an excited electron in a direct bandgap semiconductor may relax either by recombining with a hole and emitting a photon, or alternatively by scattering into a state associated with a lattice imperfection and emitting phonons, small forward bias voltages qV<<Eg may be precluded by a requirement for high external quantum efficiency ηEQE.